April 7 – 10, 2015
In the last decades, differential algebraic geometry, differential Galois theory and algebraic dynamics have benefitted from the close interaction with Model Theory, especially the model theory of fields with operators. Geometric model theory, both in the stable context and neostable counterparts, such as simplicity or o-minimality, provides an analysis of the underlying geometry of definable sets. Such an analysis is particularly powerful in combination with the Trichotomy Principle, known to hold both in differentially closed fields and in existentially closed difference fields.
Various model-theoretic tools, in particular sharpenings of the Trichotomy Principle, have been used in recent years with great success in algebraic dynamics, e.g. in connection with descent issues and the study of invariant subvarieties. Similar connections exist in the study of classical differential and difference equations, such as Painlevé equations (and its q-variants) and the differential equations satisfied by relevant analytic functions: the exponential function or the j-invariant, among others. These development relate to questions in diophantine geometry and transcendence theory.
The aim of the meeting is to present some of the major recent developments in these areas. Furthermore, we seek to bring together model-theorists and researchers in other fields of mathematics, from differential algebraic geometry to algebraic dynamics, as well as difference/differential Galois theory and arithmetic geometry.
Antoine Chambert-Loir (Université Paris-Sud)
< a target="_blank" href="http://www.cirm-math.fr/ProgWeebly/Renc1194/Moosa.pdf">Nonstandard Compact Complex Manifolds with a Generic Auto-Morphism
Newtonianity of Transseries